Evaluating risk measures: a comparative analysis of Value at Risk (VaR) and Expected Shortfall (ES)

In the realm of quantitative finance, measuring and managing market risk has been a significant challenge for both academics and practitioners. Two widely-used risk measures, Value-at-Risk and Expected Shortfall, have garnered substantial attention in the literature. This two measure of risk provide different perspectives on the potential losses that a portfolio may incur. The peculiarity of this master thesis are relative to the the comparison of VaR and ES, their advantages, limitations, and implications for risk management strategies. The recent replacement of VaR as the regulatory standard measure of risk with Expected Shortfall by the Basel Committee on Banking Supervision has heightened the importance of understanding the nuances between these two metrics. The comparative analysis presented in this master thesis will delve into the strengths and weaknesses of VaR and ES, as well as their respective implications for risk management strategies. In this thesis work we aim to address an interdisciplinary problem concerning the topic of risk measures, with particular interest on the treatment of Value-at-Risk and Expected Shortfall risk measures. This type of treatment spans many disciplines including mathematical, legal, financial and statistical in nature.